Use mathematical induction to prove the following.4n > n
What will be an ideal response?
Answers may vary. One possibility:
Sn: 4n > n
S1: 41 > 1
Sk: 4k > k
Sk+1: 4k+1 > k + 1
1. Basis step: Since 41 > 1, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
4k > k
4k ? 4 > k ? 4 Multiplying by 4, 4 > 0
4k+1 > k(1 + 3)
4k+1 > k + 3k
3k ? 1 3 ? 1 and k ? 1
4k+1 > k + 1
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